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Artículo

Characterization and computation of control invariant sets within target regionsfor linear impulsive control systems

Sánchez, Ignacio Julián RodolfoIcon ; Louembet, Christophe; Actis, Marcelo JesúsIcon ; González, Alejandro HernánIcon
Fecha de publicación: 03/2021
Editorial: Cornell University
Revista: ArXiv.org
ISSN: 2331-8422
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Matemática Aplicada

Resumen

Linear impulsively controlled systems are suitable to describe a venue of real-life problems, going from disease treatment to aerospace guidance. The main characteristic of such systems is that they remain uncontrolled for certain periods of time. As a consequence, punctual equilibria characterizations outside the origin are no longer useful, and the whole concept of equilibrium and its natural extension, the controlled invariant sets, needs to be redefined. Also, an exact characterization of the admissible states, i.e., states such that their uncontrolled evolution between impulse times remain within a predefined set, is required. An approach to such tasks -- based on the Markov-Lukasz theorem -- is presented, providing a tractable and non-conservative characterization, emerging from polynomial positivity that has application to systems with rational eigenvalues. This is in turn the basis for obtaining a tractable approximation to the maximal admissible invariant sets. In this work, it is also demonstrated that, in order for the problem to have a solution, an invariant set (and moreover, an equilibrium set) must be contained within the target zone. To assess the proposal, the so-obtained impulsive invariant set is explicitly used in the formulation of a set-based model predictive controller, with application to zone tracking. In this context, specific MPC theory needs to be considered, as the target is not necessarily stable in the sense of Lyapunov. A zone MPC formulation is proposed, which is able to i) track an invariant set such that the uncontrolled propagation fulfills the zone constraint at all times and ii) converge asymptotically to the set of periodic orbits completely contained within the target zone.
Palabras clave: IMPULSIVELY CONTROLLED SYSTEMS , INVARIANT SETS , ADMISSIBLE SETS , MODEL PREDICTIVE CONTROL , POLYNOMIAL POSITIVITY , SEMIDEFINITE PROGRAMMING
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Atribución-NoComercial-SinDerivadas 2.5 Argentina (CC BY-NC-ND 2.5 AR)
Identificadores
URI: http://hdl.handle.net/11336/167383
DOI: https://doi.org/10.48550/arXiv.2103.13831
Colecciones
Articulos(CCT - SANTA FE)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - SANTA FE
Articulos(IMAL)
Articulos de INST.DE MATEMATICA APLICADA "LITORAL"
Articulos(INTEC)
Articulos de INST.DE DES.TECNOL.PARA LA IND.QUIMICA (I)
Citación
Sánchez, Ignacio Julián Rodolfo; Louembet, Christophe; Actis, Marcelo Jesús; González, Alejandro Hernán; Characterization and computation of control invariant sets within target regionsfor linear impulsive control systems; Cornell University; ArXiv.org; 3-2021; 1-16
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